Because we use it every day, we tend to forget that our calendar is pretty strange. The year is broken up into months of different lengths, seemingly without much of a pattern. The same date can occur on different days of the week in different years. Is this really the best way to carve up a year?

In this lesson, students examine some other ways to keep track of dates, and use number sense and function concepts to convert among different calendars. What might a more reasonable calendar look like?

Students will

Convert dates among different proposed calendars using multiples and factors

Describe conversion rules in terms of functions, domain, and range

Use function composition and notation to describe two-step conversion rules

Reason about multiples and remainders to develop rules for converting dates into days of the week

Explain why functions can have inverses that fail to be functions themselves

Make recommendations for improvements to both the current and proposed calendars

Before you begin

Students should be able to reason about factors and multiples, and they should know how to obtain the remainder from a whole number division. Most of the questions revolve around function topics such as domain, range, inverses, and composition, so this lesson can serve as a way to discuss those topics in the context of calendars.

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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.

Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF)